Post-processing data

Plotting 3D data

Three dimensional flow fields are stored in Plot3D and/or VTK format and can be visualized using Paraview, or Tecplot.

Post-processing flow statistics

Mean flow statics are stored in raw format in the file stat.bin. To post-process it, use the post-processing program available in the folder tools/postpro. Compile the tool by typing,

$ make

This will produce the executable postpro.exe. An input file postpro.ini with the following variables is necessary for all flow cases.

postpro.ini

recompute_avg => integer, when recompute_avg=0 use averages calculated at runtime (in time and homogeneous spatial directions), when recompute_avg=1 calculate the time-averaged flow statistics starting from the spanwise averaged planes contained in the folder AVGZ. For channel flow cases statistics are also averaged in the streamwise direction.
it_start => integer, starting index of the spanwise averaged planes in AVGZ for computing the time averaged statistics
it_end => integer, starting index of the spanwise averaged planes in AVGZ for computing the time averaged statistics
it_out => integer, skip index of the spanwise averaged planes in AVGZ for computing the time averaged statistics. Uses every it_out plane to calculate the time-averaged flow statistics
save_plot3d => integer, when save_plot3d=1 saves 2D mean flow in plot3d format
plot3d_vars => integer, determines what variables are stored in the plot3D files (example: plot3d_vars = 1,2,3,4,13). 70 variables can be be printed:

1: \(\langle \rho \rangle\)

2: \(\langle u \rangle\)

3: \(\langle v \rangle\)

4: \(\langle w \rangle\)

5: \(\langle p \rangle\)

6: \(\langle T \rangle\)

7: \(\langle \rho^2 \rangle\)

8: \(\langle u^2 \rangle\)

9: \(\langle v^2 \rangle\)

10: \(\langle w^2 \rangle\)

11: \(\langle p^2 \rangle\)

12: \(\langle T^2 \rangle\)

13: \(\langle \rho u \rangle\)

14: \(\langle \rho v \rangle\)

15: \(\langle \rho w \rangle\)

16: \(\langle \rho u u \rangle\)

17: \(\langle \rho v v \rangle\)

18: \(\langle \rho w w \rangle\)

19: \(\langle \rho u v \rangle\)

20: \(\langle \mu \rangle\)

21: \(\langle \nu \rangle\)

22: \(\langle \omega_x^2 \rangle\)

23: \(\langle \omega_y^2 \rangle\)

24: \(\langle \omega_z^2 \rangle\)

25: \(\langle \rho T \rangle\)

26: \(\langle \rho T^2 \rangle\)

27: \(\langle T_{0} \rangle\)

28: \(\langle \rho T_{0} \rangle\)

29: \(\langle T_{0}^2 \rangle\)

30: \(\langle \rho u T \rangle\)

31: \(\langle \rho v T \rangle\)

32: \(\langle \rho w T \rangle\)

33: \(\langle Mach \rangle\)

34: \(\langle Mach^2 \rangle\)

35: \(\langle \rho u u^2 \rangle\)

36: \(\langle \rho v u^2 \rangle\)

37: \(\langle \rho u v^2 \rangle\)

38: \(\langle \rho v v^2 \rangle\)

39: \(\langle \rho u w^2 \rangle\)

40: \(\langle \rho v w^2 \rangle\)

41: \(\langle p u \rangle\)

42: \(\langle p v \rangle\)

43: \(\langle \sigma_{11} \rangle\)

44: \(\langle \sigma_{12} \rangle\)

45: \(\langle \sigma_{13} \rangle\)

46: \(\langle \sigma_{22} \rangle\)

47: \(\langle \sigma_{23} \rangle\)

48: \(\langle \sigma_{33} \rangle\)

49: \(\langle \sigma_{11} u \rangle\)

50: \(\langle \sigma_{12} u \rangle\)

51: \(\langle \sigma_{21} v \rangle\)

52: \(\langle \sigma_{22} v \rangle\)

53: \(\langle \sigma_{31} w \rangle\)

54: \(\langle \sigma_{32} w \rangle\)

55: \(\langle \sigma_{11} v + \sigma_{21} u \rangle\)

56: \(\langle \sigma_{12} v + \sigma_{22} u \rangle\)

57: \(\langle \sigma_{11} u_x + \sigma_{12} u_y + \sigma_{13} u_z \rangle\)

58: \(\langle \sigma_{21} v_x + \sigma_{22} v_y + \sigma_{23} v_z \rangle\)

59: \(\langle \sigma_{31} w_x + \sigma_{32} w_y + \sigma_{33} w_z \rangle\)

60: \(\langle \sigma_{11} v_x + \sigma_{12} (u_x + v_y) + \sigma_{22} u_y + \sigma_{13} w_z + \sigma_{23} u_z \rangle\)

61: \(\langle p u_x \rangle\)

62: \(\langle p v_y \rangle\)

63: \(\langle p w_z \rangle\)

64: \(\langle p (u_y + v_x) \rangle\)

65: \(\langle (\nabla \cdot \mathbf{u})^2 \rangle\)

66: \(\langle \rho T^2 T \rangle\)

67: \(\langle \rho T^4 \rangle\)

68: \(\langle \rho u^3 \rangle\)

69: \(\langle c_p \rangle\)

70: \(\langle \gamma \rangle\)

ixstat => list of integers, global mesh indices at which extract boundary layer profiles. Meaningful for boundary layer and airfoil flow cases.
stat_0_1 => integer, only meaningful when io_type_w == 1. When stat_0_1=0 the postprocessing tool reads statistics from the previous run , when stat_0_1=1 reads statistics from latest run
npoints_bl => integer, only meaningful for curved boundary layers and airfoils. Number of points to be used for extracting
ix_out, ix_ramp_skip => integers, only meaningful for curved boundary layers. Prints boundary layer wall quantities between ix_ramp_skip and nx-ix_ramp_skip every ix_out points.

Different files will be printed depending on the flow case that has been run.

Flow cases

Channel flow

Make sure that the file postpro.ini is present in the run folder and all the parameters have been set correctly. Copy the executable postpro.exe to the case folder you want to post-process and run:

$ ./postpro.exe

This will print the post-processed flow statistics in the folder POSTPRO/, which will contain the files channinfo.dat and channstat.prof

channinfo.dat

The file channinfo.dat contains

\(Re_\tau=u_\tau h/\nu_w\), friction Reynolds number, where \(h\) is the channel half width and \(\nu_w\) the kinematic viscosity at the wall
\(\overline{\rho}_w\) mean wall density
\(u_\tau/u_b\), ratio between friction and bulk flow velocity
\(C_f=2\overline{\tau}_w/(\rho_b u_b^2)\) skin-friction coefficient based on the mean wall shear stress, bulk flow velocity and bulk fluid density

channstat.prof

The file channstat.prof contains mean profiles of channel flow in the following format:

\(y/h,\quad\) wall-normal coordinate normalized with the channel half width
\(\overline{\rho}/\rho_b,\quad\) mean density normalized by bulk density
\(\widetilde{u}/u_b,\quad\) Mean Favre velocity normalized by bulk velocity
\(\overline{T}/T_w,\quad\) mean temperature normalized by the wall temperature
\(\overline{p}/(\rho_bu_b^2),\quad\) mean pressure normalized by twice the dynamic pressure
\(\overline{\mu}/\mu_w,\quad\) mean viscosity normalized by the wall viscosity
\(y^+,\quad\) wall-normal coordinate in viscous units
\(y_{TL}^+,\quad\) wall-normal coordinate transformed according to Trettel & Larsson [16] in viscous units (equivalent to y^*quad semi-local scaling)
\(y_{V}^+,\quad\) wall-normal coordinate transformed according to Volpiani et al. [17] in viscous units
\(u^+,\quad\) mean streamwise velocity in viscous units
\(u_{VD}^+,\quad\) mean streamwise velocity transformed according to van Driest [3] in viscous units
\(u_{TL}^+,\quad\) mean streamwise velocity transformed according to Trettel & Larsson [16] in viscous units
\(u_{V}^+,\quad\) mean streamwise velocity transformed according to Volpiani et al. [17] in viscous units
\(u_{G}^+,\quad\) mean streamwise velocity transformed according to Griffin et al. [5] in viscous units
\(u_{H}^+,\quad\) mean streamwise velocity transformed according to Hasan et al. [6] in viscous units
\(y^+du_{VD}^+/dy_{VD}^+,\quad\) van Driest indicator function
\(y_{TL}^+du_{TL}^+/dy_{TL}^+,\quad\) Trettel & Larsson log indicator function
\(y_V^+du_{V}^+/dy_V^+,\quad\) Volpiani log indicator function
\(y_G^+du_{G}^+/dy_G^+,\quad\) Griffin et al. log indicator function
\(y_H^+du_{H}^+/dy_H^+,\quad\) Hasan et al. log indicator function
\(\overline{\tau}_{11}/\tau_w,\quad\) normal Reynolds stress component 11, scaled by density, in viscous units
\(\overline{\tau}_{22}/\tau_w,\quad\) normal Reynolds stress component 22, scaled by density, in viscous units
\(\overline{\tau}_{33}/\tau_w,\quad\) normal Reynolds stress component 33, scaled by density, in viscous units
\(\overline{\tau}_{12}/\tau_w,\quad\) Reynolds shear stress component 12, scaled by density, in viscous units
\(\overline{\rho}_{rms}/(\rho_w\gamma M_\tau^2),\quad\) Density rms normalized by wall density and friction Mach number
\(\overline{T_{rms}}/(\rho_w\gamma M_\tau^2),\quad\) Temperature rms normalized by wall temperature and friction Mach number
\(\overline{p_{rms}}/\tau_w,\quad\) pressure rms normalized by wall shear stress

Curved Channel flow

Make sure that the file postpro.ini is present in the run folder and all the parameters have been set correctly. Copy the executable postpro.exe to the case folder you want to post-process and run:

$ ./postpro.exe

This will print the post-processed flow statistics in the folder POSTPRO/, which will contain the files channinfo_concave.dat, channinfo_convex.dat, channstat_concave.prof, channstat_convex.prof and channstat_global.prof, referring to the concave side, concave side, or to the two walls.

channinfo_*.dat

The files channinfo_*.dat contain

\(Re_\tau=u_\tau h/\nu_w\), friction Reynolds number, where \(h\) is the channel half width and \(\nu_w\) the kinematic viscosity at the wall
\(\overline{\rho}_w\) mean wall density
\(u_\tau/u_b\), ratio between friction and bulk flow velocity
\(C_f=2\overline{\tau}_w/(\rho_b u_b^2)\) skin-friction coefficient based on the mean wall shear stress, bulk flow velocity and bulk fluid density

channstat_concave/convex.prof

The files channstat_concave.prof and channstat_convex.prof contain mean profiles of channel flow in the following format:

\(y/h,\quad\) wall-normal coordinate normalized with the channel half width
\(\overline{\rho}/\rho_b,\quad\) mean density normalized by bulk density
\(\widetilde{u}/u_b,\quad\) Mean Favre velocity normalized by bulk velocity
\(\overline{T}/T_w,\quad\) mean temperature normalized by the wall temperature
\(\overline{p}/(\rho_bu_b^2),\quad\) mean pressure normalized by twice the dynamic pressure
\(\overline{\mu}/\mu_w,\quad\) mean viscosity normalized by the wall viscosity
\(y^+,\quad\) wall-normal coordinate in viscous units
\(y_{TL}^+,\quad\) wall-normal coordinate transformed according to Trettel & Larsson [16] in viscous units (equivalent to y^*quad semi-local scaling)
\(y_{V}^+,\quad\) wall-normal coordinate transformed according to Volpiani et al. [17] in viscous units
\(u^+,\quad\) mean streamwise velocity in viscous units
\(u_{VD}^+,\quad\) mean streamwise velocity transformed according to van Driest [3] in viscous units
\(u_{TL}^+,\quad\) mean streamwise velocity transformed according to Trettel & Larsson [16] in viscous units
\(u_{V}^+,\quad\) mean streamwise velocity transformed according to Volpiani et al. [17] in viscous units
\(u_{H}^+,\quad\) mean streamwise velocity transformed according to Hasan et al. [6] in viscous units
\(\overline{\tau}_{11}/\tau_w,\quad\) normal Reynolds stress component 11, scaled by density, in viscous units
\(\overline{\tau}_{22}/\tau_w,\quad\) normal Reynolds stress component 22, scaled by density, in viscous units
\(\overline{\tau}_{33}/\tau_w,\quad\) normal Reynolds stress component 33, scaled by density, in viscous units
\(\overline{\tau}_{12}/\tau_w,\quad\) Reynolds shear stress component 12, scaled by density, in viscous units
\(\overline{\rho}/\rho_w,\quad\) mean density normalized by bulk density
\(\overline{\rho}_{rms}/(\rho_w\gamma M_\tau^2),\quad\) Density rms normalized by wall density and friction Mach number
\(\overline{T_{rms}}/(\rho_w\gamma M_\tau^2),\quad\) Temperature rms normalized by wall temperature and friction Mach number
\(\overline{p_{rms}}/\tau_w,\quad\) pressure rms normalized by wall shear stress

channstat_global.prof

The file channstat_global.prof contains mean profiles of channel flow in the following format: 1. \(y/h,\quad\) wall-normal coordinate normalized with the channel half width 2. \(\widetilde{u}/u_b,\quad\) Favre-averaged streamwise velocity component 3. \(\overline{u}/u_b,\quad\) Reynolds-averaged averaged streamwise velocity component 4. \(\overline{\tau}_{11}/\tau_w,\quad\) normal Reynolds stress component 11, scaled by density, in viscous units 5. \(\overline{\tau}_{22}/\tau_w,\quad\) normal Reynolds stress component 22, scaled by density, in viscous units 6. \(\overline{\tau}_{33}/\tau_w,\quad\) normal Reynolds stress component 33, scaled by density, in viscous units 7. \(\overline{\tau}_{12}/\tau_w,\quad\) Reynolds shear stress component 12, scaled by density, in viscous units

Boundary layer

Make sure that the file postpro.ini is present in the run folder and all the parameters have been set correctly.

Run the post-processing tool by typing:

$ ./postpro.exe

The post-processing routine will create the folder POSTPRO, containing the files cf.dat and stat_nnnnn.dat, where nnnnn is the global i-index.

cf.dat

The file cf.dat contains the boundary layer characteristics as a function of the streamwise direction:

\(x/\delta_0,\quad\) streamwise coordinate normalized by inflow boundary layer thickness
\(\delta_{99}/{\delta_{99}}_{in},\quad\) boundary layer thickness
\(\delta^*,\quad\) displacement thickness
\(\theta^*,\quad\) momentum thickness
\(\delta_i^*,\quad\) incompressible displacement thickness
\(\theta_i^*,\quad\) incompressible momentum thickness
\(H,\quad\) shape factor
\(H_i,\quad\) incompressible shape factor
\(\rho_w/\rho_{\infty},\quad\) Wall density
\(T_w/T_\infty,\quad\) Wall temperature
\(p_w/p_\infty,\quad\) Wall pressure
\(p_{rms}/\tau_w,\quad\) Wall pressure rms
\(u_\tau/u_\infty,\quad\) friction velocity
\(Cf=\overline{\tau}_w/(\rho_w U_\infty^2),\quad\) friction coefficient
\(Cf_i=\overline{\tau}_w/(\rho_w U_\infty^2),\quad\) incompressible friction coefficient, based on Van Driest II transformation [4]
\(Re_{\delta_{99}}=u_\inf\delta_{99}/\nu_\infty,\quad\) Reynolds number based on the boundary layer thickness
\(Re_{\theta}=u_\inf\theta/\nu_\infty,\quad\) Reynolds number based on the momentum thickness
\(Re_{\delta_2}=\rho_\inf u_\inf\theta/\mu_w,\quad\) Reynolds number based on the momentum thickness and wall viscosity
\(Re_\tau=\delta_{99}/\delta_v,\quad\) friction Reynolds number
\(B_q=q_w/(\rho_wC_pu_\tau T_w),\quad\) heat flux coefficient
\(c_h=q_w/[\rho_wC_pu_\tau (T_w-T_r)],\quad\) Stanton number

stat_nnnnn.dat

The files stat_nnnnn.dat contain the boundary layer profiles in the following format:

\(y/{\delta_{99}}_{in},\quad\) wall-distance normalized by boundary layer thickness at the inflow
\(\overline{\rho}/\overline{\rho}_\infty,\quad\) mean density
\(\widetilde{u}/u_0,\quad\) mean streamwise velocity
\(\widetilde{v}/u_0,\quad\) mean wall-normal velocity
\(\widetilde{T}/T_\infty,\quad\) Mean temperature
\(\overline{p}/p_\infty,\quad\) Mean pressure
\(\overline{\mu}/\mu_w,\quad\) Mean viscosity normalized by the wall viscosity
\(y/\delta_{99},\quad\) wall-distance normalized by local boundary layer thickness
\(y^+,\quad\) wall-distance in viscous units
\(y_{TL},\quad\) wall-distance transformed according to Trettel & Larsson [16], in viscous units
\(y_V,\quad\) wall-distance transformed according to Volpiani el al. [17], in viscous units
\(\widetilde{u}^+,\quad\) streamwise velocity in viscous units
\(u_{VD}^+,\quad\) streamwise velocity transformed according to van Driest [3], in viscous units
\(u_{TL}^+,\quad\) mean streamwise velocity transformed according to Trettel & Larsson [16], in viscous units
\(u_{V}^+,\quad\) mean streamwise velocity transformed according to Volpiani et al. [17], in viscous units
\(u_{G}^+,\quad\) mean streamwise velocity transformed according to Griffin et al. [5], in viscous units
\(u_{H}^+,\quad\) mean streamwise velocity transformed according to Hasan et al. [6], in viscous units
\(y^+du_{VD}^+/dy_{VD}^+,\quad\) van Driest indicator function
\(y_{TL}^+du_{TL}^+/dy_{TL}^+,\quad\) Trettel & Larsson log indicator function
\(y_V^+du_{V}^+/dy_V^+,\quad\) Volpiani log indicator function
\(y_G^+du_{G}^+/dy_G^+,\quad\) Griffin et al. log indicator function
\(y_H^+du_{H}^+/dy_H^+,\quad\) Hasan et al. log indicator function
\(\overline{\tau}_{11}/\tau_w,\quad\) normal Reynolds stress component 11, scaled by density, in viscous units
\(\overline{\tau}_{22}/\tau_w,\quad\) normal Reynolds stress component 22, scaled by density, in viscous units
\(\overline{\tau}_{33}/\tau_w,\quad\) normal Reynolds stress component 33, scaled by density, in viscous units
\(\overline{\tau}_{12}/\tau_w,\quad\) Reynolds shear stress component 12, scaled by density, in viscous units
\(\rho_{rms}/(\rho_w\gamma M_\tau^2),\quad\) density rms
\(T_{rms}/(T_w\gamma M_\tau^2),\quad\) temperature rms
\(p_{rms}/\tau_w,\quad\) pressure rms in wall units

Curved boundary layer

Make sure that the file postpro.ini is present in the run folder and all the parameters have been set correctly.

Run the post-processing tool by typing:

$ ./postpro.exe

The post-processing routine will create the folder POSTPRO, containing the files cf.dat and stat_nnnnn.dat, where nnnnn is the global i-index.

cf.dat

The file cf.dat contains the boundary layer characteristics as a function of the streamwise direction:

\(x/\delta_0,\quad\) x-coordinate of the wall, normalized by inflow boundary layer thickness
\(y/\delta_0,\quad\) y-coordinate of the wall, normalized by inflow boundary layer thickness
\(\delta_{99}/{\delta_{99}}_{in},\quad\) boundary layer thickness based on 0.99 u_infty
\(\delta/{\delta_{99}}_{in},\quad\) boundary layer thickness based on vorticity magnitude
\(\delta^*,\quad\) displacement thickness
\(\theta^*,\quad\) momentum thickness
\(\delta_i^*,\quad\) incompressible displacement thickness
\(\theta_i^*,\quad\) incompressible momentum thickness
\(H,\quad\) shape factor
\(H_i,\quad\) incompressible shape factor
\(\rho_w/\rho_{\infty},\quad\) Wall density
\(T_w/T_\infty,\quad\) Wall temperature
\(p_w/p_\infty,\quad\) Wall pressure
\(p_{rms}/\tau_w,\quad\) Wall pressure rms
\(\delta_v,\quad\) viscous length scale
\(u_\tau,\quad\) friction velocity
\(\tau_w,\quad\) wall shear stress
\(Cf=\overline{\tau}_w/(\rho_w U_\infty^2),\quad\) friction coefficient
\(Cf_i=\overline{\tau}_w/(\rho_w U_\infty^2),\quad\) incompressible friction coefficient, based on Van Driest II transformation [4]
\(u_e/u_\infty,\quad\) Ratio between external velocity (0.99u_infty) and nominal free-stream velocity
\(u_e/u_\infty,\quad\) Ratio between external velocity (u(delta_{99})) and nominal free-stream velocity
\(Re_{\delta_{99}}=u_\inf\delta_{99}/\nu_\infty,\quad\) Reynolds number based on the boundary layer thickness
\(Re_{\theta}=u_\inf\theta/\nu_\infty,\quad\) Reynolds number based on the momentum thickness
\(Re_{\delta_2}=\rho_\inf u_\inf\theta/\mu_w,\quad\) Reynolds number based on the momentum thickness and wall viscosity
\(Re_\tau=\delta_{99}/\delta_v,\quad\) friction Reynolds number
\(B_q=q_w/(\rho_wC_pu_\tau T_w),\quad\) heat flux coefficient
\(c_h=q_w/[\rho_wC_pu_\tau (T_w-T_r)],\quad\) Stanton number

stat_nnnnn.dat

The files stat_nnnnn.dat contain the boundary layer profiles in the following format:

\(y/{\delta_{99}}_{in},\quad\) wall-distance normalized by boundary layer thickness at the inflow
\(\overline{\rho}/\overline{\rho}_\infty,\quad\) mean density
\(\widetilde{u}/u_0,\quad\) mean Cartesian velocity in x-direction
\(\widetilde{v}/u_0,\quad\) mean Cartesian velocity in y-direction
\(\widetilde{u}/u_0,\quad\) mean wall-parallel velocity
\(\widetilde{v}/u_0,\quad\) mean wall-normal velocity
\(\widetilde{T}/T_\infty,\quad\) Mean temperature
\(\overline{p}/p_\infty,\quad\) Mean pressure
\(\overline{\mu}/\mu_w,\quad\) Mean dynamic viscosity normalized by the wall viscosity
\(y/\delta_{99},\quad\) wall-distance normalized by local boundary layer thickness
\(y^+,\quad\) wall-distance in viscous units
\(y_{TL},\quad\) wall-distance transformed according to Trettel & Larsson [16], in viscous units
\(y_V,\quad\) wall-distance transformed according to Volpiani el al. [17], in viscous units
\(\widetilde{u}^+,\quad\) streamwise velocity in viscous units
\(u_{VD}^+,\quad\) streamwise velocity transformed according to van Driest [3], in viscous units
\(u_{TL}^+,\quad\) mean streamwise velocity transformed according to Trettel & Larsson [16], in viscous units
\(u_{V}^+,\quad\) mean streamwise velocity transformed according to Volpiani et al. [17], in viscous units
\(u_{H}^+,\quad\) mean streamwise velocity transformed according to Hasan et al. [6], in viscous units
\(\overline{\tau}_{11}/\tau_w,\quad\) normal Reynolds stress component 11, scaled by density, in viscous units
\(\overline{\tau}_{22}/\tau_w,\quad\) normal Reynolds stress component 22, scaled by density, in viscous units
\(\overline{\tau}_{33}/\tau_w,\quad\) normal Reynolds stress component 33, scaled by density, in viscous units
\(\overline{\tau}_{12}/\tau_w,\quad\) Reynolds shear stress component 12, scaled by density, in viscous units
\(\rho_{rms}/(\rho_w\gamma M_\tau^2),\quad\) density rms
\(T_{rms}/(T_w\gamma M_\tau^2),\quad\) temperature rms
\(p_{rms}/p_0,\quad\) pressure rms in outer units

Airfoil

Make sure that the file postpro.ini is present in the run folder and all the parameters have been set correctly.

Run the post-processing tool by typing:

$ ./postpro.exe

The post-processing routine will create the folder POSTPRO, containing the files avg_forces.dat, bl_pressure.dat bl_suction.dat and stat_nnnnn.dat, where nnnnn is the global i-index.

avg_coeff.dat

The file avg_coeff.dat contains the boundary layer characteristics as a function of the streamwise direction:

\(c_L=L/(0.5\rho_\infty u_\infty^2)\) Lift coefficient per unit chord
\(c_D=D/(0.5\rho_\infty u_\infty^2)\) Drag coefficient per unit chord
\(c_p=(\oint_s p\mathbf{n} \cdot \mathrm{d}\mathbf{s})/(0.5\rho_\infty u_\infty^2)\) Integrated wall pressure normalized by the dynamic pressure
\(c_f=(\oint_s \boldsymbol{\tau}_w\cdot \mathrm{d}\mathbf{s})/(0.5\rho_\infty u_\infty^2)\) Integrated wall-shear stress normalized by the dynamic pressure

bl_suction.dat/bl_pressure.dat

The files bl_pressure/bl_suction.dat contain the airfoil boundary layer characteristics as a function of the streamwise direction:

\(x/\delta_0,\quad\) x-coordinate of the wall, normalized by inflow boundary layer thickness
\(y/\delta_0,\quad\) y-coordinate of the wall, normalized by inflow boundary layer thickness
\(\delta_{99}/{\delta_{99}}_{in},\quad\) boundary layer thickness based on 0.99 u_infty
\(\delta/{\delta_{99}}_{in},\quad\) boundary layer thickness based on vorticity magnitude
\(\delta^*,\quad\) displacement thickness
\(\theta^*,\quad\) momentum thickness
\(\delta_i^*,\quad\) incompressible displacement thickness
\(\theta_i^*,\quad\) incompressible momentum thickness
\(H,\quad\) shape factor
\(H_i,\quad\) incompressible shape factor
\(\rho_w/\rho_{\infty},\quad\) Wall density
\(T_w/T_\infty,\quad\) Wall temperature
\(p_w/p_\infty,\quad\) Wall pressure
\(p_{rms}/\tau_w,\quad\) Wall pressure rms
\(\delta_v,\quad\) viscous length scale
\(u_\tau,\quad\) friction velocity
\(\tau_w,\quad\) wall shear stress
\(Cf=\overline{\tau}_w/(\rho_w U_\infty^2),\quad\) friction coefficient
\(Cf_i=\overline{\tau}_w/(\rho_w U_\infty^2),\quad\) incompressible friction coefficient, based on Van Driest II transformation [4]
\(c_p,\quad\) Pressure coefficient
\(u_e/u_\infty,\quad\) Ratio between external velocity (0.99u_infty) and nominal free-stream velocity
\(u_{99}/u_\infty,\quad\) Ratio between external velocity (u(delta_{99})) and nominal free-stream velocity
\(Re_{\delta_{99}}=u_\inf\delta_{99}/\nu_\infty,\quad\) Reynolds number based on the boundary layer thickness
\(Re_{\theta}=u_\inf\theta/\nu_\infty,\quad\) Reynolds number based on the momentum thickness
\(Re_{\delta_2}=\rho_\inf u_\inf\theta/\mu_w,\quad\) Reynolds number based on the momentum thickness and wall viscosity
\(Re_\tau=\delta_{99}/\delta_v,\quad\) friction Reynolds number
\(B_q=q_w/(\rho_wC_pu_\tau T_w),\quad\) heat flux coefficient
\(c_h=q_w/[\rho_wC_pu_\tau (T_w-T_r)],\quad\) Stanton number
\(j_\omega,\quad\) index of the wall-normal mesh coordinate corresponding to the boundary layer thickness based on the vorticity criterion
\(j_\omega,\quad\) index of the wall-normal mesh coordinate corresponding to the boundary layer thickness based on \(u_{99}\)

stat_nnnnn.dat

The files stat_nnnnn.dat contain the boundary layer profiles in the following format:

\(y/{\delta_{99}}_{in},\quad\) wall-distance normalized by boundary layer thickness at the inflow
\(\overline{\rho}/\overline{\rho}_\infty,\quad\) mean density
\(\widetilde{u}/u_0,\quad\) mean Cartesian velocity in x-direction
\(\widetilde{v}/u_0,\quad\) mean Cartesian velocity in y-direction
\(\widetilde{u_\parallel/u_0,\quad\) mean wall-parallel velocity
\(\widetilde{v}_\perp/u_0,\quad\) mean wall-normal velocity
\(\widetilde{T}/T_\infty,\quad\) Mean temperature
\(\overline{p}/p_\infty,\quad\) Mean pressure
\(\overline{\mu}/\mu_w,\quad\) Mean dynamic viscosity normalized by the wall viscosity
\(y/\delta_{99},\quad\) wall-distance normalized by local boundary layer thickness
\(y^+,\quad\) wall-distance in viscous units
\(y_{TL},\quad\) wall-distance transformed according to Trettel & Larsson [16], in viscous units
\(y_V,\quad\) wall-distance transformed according to Volpiani el al. [17], in viscous units
\(\widetilde{u}^+,\quad\) streamwise velocity in viscous units
\(u_{VD}^+,\quad\) streamwise velocity transformed according to van Driest [3], in viscous units
\(u_{TL}^+,\quad\) mean streamwise velocity transformed according to Trettel & Larsson [16], in viscous units
\(u_{V}^+,\quad\) mean streamwise velocity transformed according to Volpiani et al. [17], in viscous units
\(u_{H}^+,\quad\) mean streamwise velocity transformed according to Hasan et al. [6], in viscous units
\(\overline{\tau}_{11}/\tau_w,\quad\) normal Reynolds stress component 11, scaled by density, in viscous units
\(\overline{\tau}_{22}/\tau_w,\quad\) normal Reynolds stress component 22, scaled by density, in viscous units
\(\overline{\tau}_{33}/\tau_w,\quad\) normal Reynolds stress component 33, scaled by density, in viscous units
\(\overline{\tau}_{12}/\tau_w,\quad\) Reynolds shear stress component 12, scaled by density, in viscous units
\(\rho_{rms}/(\rho_w\gamma M_\tau^2),\quad\) density rms
\(T_{rms}/(T_w\gamma M_\tau^2),\quad\) temperature rms
\(p_{rms}/p_0,\quad\) pressure rms in outer units